Now showing items 1-13 of 13

• #### Breakdown of a 2D heteroclinic connection in the hopf-zero singularity (I) ﻿

(2018-10-01)
Article
Open Access
In this paper we study a beyond all orders phenomenon which appears in the analytic unfoldings of the Hopf-zero singularity. It consists in the breakdown of a two-dimensional heteroclinic surface which exists in the truncated ...
• #### Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (II): The generic case ﻿

(2018-04-17)
Article
Open Access
In this paper, we prove the breakdown of the two-dimensional stable and unstable manifolds associated to two saddle-focus points which appear in the unfoldings of the Hopf-zero singularity. The method consists in obtaining ...
• #### Breakdown of heteroclinic orbits for analytic unfoldings of the hopf-zero singularity. The singular case ﻿

(2011)
External research report
Open Access
In this paper we prove the breakdown of an heteroclinic connection in the analytic versal unfoldings of the generic Hopf-Zero singularity. This heteroclinic orbit appears at any order if one performs the normal form around ...
• #### Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity ﻿

(2004)
Article
Open Access
In this paper we study the exponentially small splitting of a heteroclinic orbit in some unfoldings of the central singularity also called Hopf-zero singularity. The fields under consideration are of the form: dx dτ = ...
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2018-01-18)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2017-11-03)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES | ( Examen final ) ﻿

(Universitat Politècnica de Catalunya, 2019-01-10)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES | ( Examen parcial ) ﻿

(Universitat Politècnica de Catalunya, 2018-11-09)
Exam
• #### Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity ﻿

(2013)
Article
Restricted access - publisher's policy
In this paper we prove the breakdown of a heteroclinic connection in the analytic versal unfoldings of the generic Hopf-zero singularity in an open set of the parameter space. This heteroclinic orbit appears at any order ...
• #### Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results ﻿

(2011)
External research report
Open Access
In this paper we study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation which is fast and periodic in time. We provide ...
• #### Gevrey estimates for one dimensional parabolic invariant manifolds of non-hyperbolic fixed points ﻿

(2017-08-01)
Article
Open Access
We study the Gevrey character of a natural parameterization of one dimensional invariant manifolds associated to a parabolic direction of fixed points of analytic maps, that is, a direction associated with an eigenvalue ...
• #### On the asymptotic wavenumber of spiral waves in lambda - omega systems ﻿

(2016-01-01)
Article
Open Access
In this paper we consider spiral wave solutions of a general class of $\lambda -\omega$ systems with a small twist parameter q and we prove that the asymptotic wavenumber of the spirals is a ${{\mathcal{C}}^{\infty}}$ ...
• #### Whiskered parabolic tori in the planar (n+ 1) -body problem ﻿

(2019-01-01)
Article
Restricted access - publisher's policy
The planar (n+1)-body problem models the motion of n+1 bodies in the plane under their mutual Newtonian gravitational attraction forces. When n=3, the question about final motions, that is, what are the possible limit ...